DZY Loves Sequences

最新推荐文章于 2021-10-15 13:15:45 发布

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最新推荐文章于 2021-10-15 13:15:45 发布

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原文链接：http://www.cnblogs.com/llei1573/p/3852959.html

本文介绍了一种寻找最长递增子序列的算法，通过处理输入序列并利用动态规划思想来找出可更改一个数使子序列严格递增的最长长度。文章提供了完整的C++代码实现，并通过样例输入输出展示其正确性。

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DZY has a sequence a, consisting of n integers.

We'll call a sequence ai, ai + 1, ..., aj (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.

Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.

You only need to output the length of the subsegment you find.

Input

The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

In a single line print the answer to the problem — the maximum length of the required subsegment.

Sample test(s)

input

6
7 2 3 1 5 6

output

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
#define N 100005
#define INF 0x3f3f3f3f
int a[N],b[N],c[N];
int main()
{
    int n,i;
    while(~scanf("%d",&n))
    {
        memset(c,0,sizeof(c));
        memset(b,0,sizeof(b));
        for(i = 1; i<= n ; i++) scanf("%d",&a[i]);
        b[1] = 1;
        for(i = 2 ; i <= n ; i++){
            if(a[i]>a[i-1]) b[i] = b[i-1]+1;
            else b[i] = 1;
        }
        c[n] = 1;
        for(i = n-1 ; i>=1 ; i--){
            if(a[i]<a[i+1]) c[i] = c[i+1] +1;
            else c[i] = 1;
        }
        int ans = max(c[2]+1,b[n-1]+1);
        for(i = 2 ; i < n ; i++){
            if(a[i+1]>a[i-1]+1) ans = max(ans,b[i-1]+c[i+1]+1);
            else ans = max(ans,max(b[i-1]+1,c[i+1]+1));
        }
        printf("%d\n",ans);
    }
    return 0;
}